Inference about the performance of Fisher's linear discriminant function

Abstract

In the early seventies it was observed that discriminatory values obtained by the leaving-one-out method tend to degrade if the number of variables becomes large. The actual discriminatory value D_a of Fisher's linear discriminant function was introduced to understand this phenomenon. During the eighties progress was made concerning inference about D_a, which is of interest for selection-of-variables purposes. Exact expectations were derived and, more importantly, it was observed that exact inferences are possible if certain parameters are specified. Considerable work was also done, especially by Khatri, to replace the normality assumptions by more general ones. The paper describes the history of the subject and introduces the reader to the present state of the art.